Title:

The equivalence of convergence results between modified Ishikawa and modified Mann iterations

Creator:

Mogbademu, A. A. ; Kim, J. K.

Subject and Keywords:

modified Mann iteration process with errors ; Modified Ishikawa iteration process with error ; Banach space ; fixed point ; nearly weak uniformly L-Lipschitzian

Abstract:

In [11], the author discussed a new class of nearly weak uniformly L-Lipschitzian mappings and prove some strong convergence results of the modified Ishikawa iteration with errors in real Banach spaces. And the author has given the open problem as follows: Are there any difference on convergence between the Mann iteration and Ishikawa iteration? Can we prove the equivalence on convergence between these two iterations? In this paper, we given an affirmative answer to the open problem.

Publisher:

Publishing House of Poznan University of Technology

Place of publication:

Poznań

Object type:

artykuł

ISBN/ISSN:

0044-4413

DOI:

10.21008/j.0044-4413.2019.0008

Language:

eng

Format:

pp. 93-102

Rights holder:

Politechnika Poznańska